The IMA Volumes in Mathematics and its Applications

Compatible Spatial Discretizations

Editors: Arnold, D.N., Bochev, P.B., Lehoucq, R.B., Nicolaides, R.A., Shashkov, M. (Eds.)

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About this book

The IMA Hot Topics workshop on compatible spatialdiscretizations was held May 11-15, 2004 at the University of Minnesota. The purpose of the workshop was to bring together scientists at the forefront of the research in the numerical solution of PDEs to discuss recent advances and novel applications of geometrical and homological approaches to discretization. This volume contains original contributions based on the material presented at the workshop. A unique feature of the collection is the inclusion of work that is representative of the recent developments in compatible discretizations across a wide spectrum of disciplines in computational science.

Compatible spatial discretizations are those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. The papers in the volume offer a snapshot of the current trends and developments in compatible spatial discretizations. The reader will find valuable insights on spatial compatibility from several different perspectives and important examples of applications compatible discretizations in computational electromagnetics, geosciences, linear elasticity, eigenvalue approximations and MHD. The contributions collected in this volume will help to elucidate relations between different methods and concepts and to generally advance our understanding of compatible spatial discretizations for PDEs. Abstracts and presentation slides from the workshop can be accessed at http://www.ima.umn.edu/talks/workshops/5-11-15.2004/.

Table of contents (11 chapters)

Table of contents (11 chapters)
  • Numerical Convergence of the MPFA O-Method for General Quadrilateral Grids in Two and Three Dimensions

    Pages 1-21

    Aavatsmark, Ivar (et al.)

  • Differential Complexes and Stability of Finite Element Methods I. The de Rham Complex

    Pages 23-46

    Arnold, Douglas N. (et al.)

  • Defferential Complexes and Stability of Finite Element Methods II: The Elasticity Complex

    Pages 47-67

    Arnold, Douglas N. (et al.)

  • On the Role of Involutions in the Discontinuous Galerkin Discretization of Maxwell and Magnetohydrodynamic Systems

    Pages 69-88

    Barth, Timothy

  • Principles of Mimetic Discretizations of Differential Operators

    Pages 89-119

    Bochev, Pavel B. (et al.)

Buy this book

eBook $149.00
price for USA in USD
  • ISBN 978-0-387-38034-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $199.99
price for USA in USD
  • ISBN 978-0-387-30916-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $199.99
price for USA in USD
  • ISBN 978-1-4939-0197-5
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Compatible Spatial Discretizations
Editors
  • Douglas N. Arnold
  • Pavel B. Bochev
  • Richard B. Lehoucq
  • Roy A. Nicolaides
  • Mikhail Shashkov
Series Title
The IMA Volumes in Mathematics and its Applications
Series Volume
142
Copyright
2006
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-38034-6
DOI
10.1007/0-387-38034-5
Hardcover ISBN
978-0-387-30916-3
Softcover ISBN
978-1-4939-0197-5
Series ISSN
0940-6573
Edition Number
1
Number of Pages
XIV, 247
Topics